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The estimation of the covariance structure from a discretely observed multivariate Gaussian process under asynchronicity and noise is analysed under high-frequency asymptotics. Asymptotic lower and upper bounds are established for a general…

The article investigates an algorithm for identifying an unknown constant parameter for a scalar regression model using a nonlinear operator that allows us to obtain a new regression equation (with an expanded number of unknown parameters)…

Scaled sparse linear regression jointly estimates the regression coefficients and noise level in a linear model. It chooses an equilibrium with a sparse regression method by iteratively estimating the noise level via the mean residual…

This paper focuses on the problem of pitch tracking in noisy conditions. A method using harmonic information in the residual signal is presented. The proposed criterion is used both for pitch estimation, as well as for determining the…

This paper considers least-square based estimation of the amplitude and square amplitude of a quantized sine wave, done by considering random initial record phase. Using amplitude- and frequency-domain modeling techniques, it is shown that…

Stacking regressions is an ensemble technique that forms linear combinations of different regression estimators to enhance predictive accuracy. The conventional approach uses cross-validation data to generate predictions from the…

A continuous-time regression model with a jointly strictly sub-Gaussian random noise is considered in the paper. Upper exponential bounds for probabilities of large deviations of the least squares estimator for the regression parameter are…

In the context of nonparametric regression, we study conditions under which the consistency (and rates of convergence) of estimators built from discretely sampled curves can be derived from the consistency of estimators based on the…

We develop expressions for the nonlinear wave damping and frequency correction of a field of random, spatially homogeneous, acoustic waves. The implications for the nature of the equilibrium spectral energy distribution are discussed

We consider the problem of estimating the structural function in nonparametric instrumental regression, where in the presence of an instrument W a response Y is modeled in dependence of an endogenous explanatory variable Z. The proposed…

We revisit a model for time-varying linear regression that assumes the unknown parameters evolve according to a linear dynamical system. Counterintuitively, we show that when the underlying dynamics are stable the parameters of this model…

Residual variance and the signal-to-noise ratio are important quantities in many statistical models and model fitting procedures. They play an important role in regression diagnostics, in determining the performance limits in estimation and…

We consider the problem of least squares parameter estimation from single-trajectory data for discrete-time, unstable, closed-loop nonlinear stochastic systems, with linearly parameterised uncertainty. Assuming a region of the state space…

We prove a new and general concentration inequality for the excess risk in least-squares regression with random design and heteroscedastic noise. No specific structure is required on the model, except the existence of a suitable function…

We present a sample- and time-efficient differentially private algorithm for ordinary least squares, with error that depends linearly on the dimension and is independent of the condition number of $X^\top X$, where $X$ is the design matrix.…

The Hodgkin-Huxley equations constitute one of the more realistic neuronal models in literature and the most accepted one. It is well known that, depending on the value of the external stimuli current, it exhibits periodic solutions, both…

We consider the nonparametric robust estimation problem for regression models in continuous time with semi-Markov noises. An adaptive model selection procedure is proposed. Under general moment conditions on the noise distribution a sharp…

We discuss nonparametric estimation of linear multiplier in a trend coefficient in models governed by an $\alpha$-stable small noise.

We consider the problem of recovering of continuous multi-dimensional functions from the noisy observations over the regular grid. Our focus is at the adaptive estimation in the case when the function can be well recovered using a linear…

For some estimations and predictions, we solve minimization problems with asymmetric loss functions. Usually, we estimate the coefficient of regression for these problems. In this paper, we do not make such the estimation, but rather give a…